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[[62,18,7]] d ≤
n
62
k
18
d
7
kd²/n
14.2258
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 7, d_Z ≤ 7 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 7 · witness weight 7 (claimed upper_bound)
witness found by @MathysRennela · research/kit/surrogate.lightest_logical · found at 300 trials · survived 300 trials · 2026-11-07
witness operator (support, 7 qubits)
[0, 14, 22, 29, 43, 49, 55]
d_Z 7 · witness weight 7 (claimed upper_bound)
witness found by @MathysRennela · research/kit/surrogate.lightest_logical · found at 300 trials · survived 300 trials · 2026-11-07
witness operator (support, 7 qubits)
[9, 14, 20, 38, 40, 53, 54]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 7–8 (mean 7.909) · H_Z 7–8 (mean 7.864)
qubit degrees H_X 1–4 (mean 2.806) · H_Z 1–4 (mean 2.79)
trapping sets H_X (1,1)×3 (2,1)×4 (3,1)×11 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,1): 3 (1,2): 17 (1,3): 31 (1,4): 11 (2,1): 4 (2,2): 30 (2,3): 129 (2,4): 242 (2,5): 165 (2,6): 32 (3,1): 11 (3,2): 103 (3,3): 529 (3,4): 1608 (3,5): 2558 (3,6): 2164 (3,7): 1060 (3,8): 409 (3,9): 99 (3,10): 11
trapping sets H_Z (1,1)×3 (2,1)×2 (3,1)×15 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,1): 3 (1,2): 20 (1,3): 26 (1,4): 13 (2,1): 2 (2,2): 38 (2,3): 131 (2,4): 213 (2,5): 169 (2,6): 42 (3,1): 15 (3,2): 106 (3,3): 576 (3,4): 1529 (3,5): 2408 (3,6): 2048 (3,7): 1190 (3,8): 420 (3,9): 124 (3,10): 13

Circuit tier

syndrome-extraction memory circuits committed under circuits/62-18-7-b/ · canonical noise recipe, 7 rounds, stim 1.16.0
d_circ ≤ 4 (min over bases; penalty-only, clamped to ≤ d)
d_circ^X 4 · fault-set witness of 4 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 4)
[2827, 2837, 3375, 3377]
d_circ^Z 4 · fault-set witness of 4 mechanisms (claimed upper_bound)
witness fault set (mechanism indices in the committed .dem, 4)
[15878, 15884, 15959, 15974]
no measured logical error rate yet; d_circ is a floor, and the measured tier records the prefactor it cannot see

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction code-calculus v0.1 E-PEEL of a CSS parent
model Beam 1.0 (claimed, not verified)
date 2026-11-07
family other (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[62,18,7]] — code-calculus v0.1 E-PEEL of a CSS parent

Direction & hypothesis

Targeted a Pareto opening in the unrestricted / weight-8 cell via the priced construction calculus (unitaryfoundation/code-calculus v0.1): E-PEEL a qubit (or check) of a CSS parent, recomputing ranks, connectivity, and max check weight. The child is board-advancing when its (n,k,d,w) is nondominated in its cell.

What was searched

Single-step E-PEEL moves over CSS parents, screened structurally (no bare qubit, connected Tanner graph, independent displayed rows) and by an optimistic 4-axis domination test against the board before any witness search. Survivors were packaged with research/kit/submit.py (make_submission, save_submission) and validated with research/kit/coordination.py gate (passed: true).

Evidence trail

Distance is a witness-backed upper bound from a 300-trial RIS screen per side (confidence upper_bound); no lower bound is claimed. Move: E-PEEL of parent 63-18-7.

Dead ends

Other moves and parents in the same sweep were dominated in their cell and discarded before gating.

Tools

Model: Beam 1.0. Author: @mathysrennela. Harness: OpenCode. Repo tooling: research/kit/submit.py, research/kit/coordination.py, research/kit/prescreen.py, verify/validate_candidate.py.

Reproduction

Load the parent CSS entry, build a CodeState via CodeState.from_challenge, enumerate E-PEEL candidates with the code-calculus planner, apply with apply_operation, and package the surviving child with make_submission. Library: github.com/MathysRennela/code-calculus (v0.1).

Parity checks

X-checks 22 (max weight 8) · Z-checks 22 (max weight 8)
H_X (22 checks, sparse supports)
[0, 8, 12, 30, 31, 40, 53, 59] [0, 1, 18, 23, 32, 43, 46, 57] [0, 2, 17, 19, 33, 39, 49, 56] [3, 19, 23, 27, 34, 42, 51] [1, 4, 24, 26, 35, 41, 49, 52] [2, 5, 21, 25, 32, 36, 48, 61] [1, 2, 3, 6, 31, 37, 55, 60] [3, 7, 12, 26, 38, 48, 54, 56] [4, 8, 27, 29, 36, 39, 47, 55] [5, 6, 9, 10, 33, 35, 40] [3, 8, 10, 25, 41, 46, 50, 58] [4, 6, 7, 11, 32, 42, 45, 59] [5, 12, 27, 28, 37, 43, 44, 52] [7, 13, 18, 29, 33, 44, 58, 60] [10, 14, 17, 28, 38, 45, 55, 57] [9, 11, 15, 16, 37, 39, 46, 54] [0, 7, 10, 16, 34, 47, 52, 61] [8, 11, 13, 17, 35, 43, 48, 51] [9, 12, 14, 18, 36, 42, 49, 50] [13, 19, 24, 30, 37, 45, 50, 61] [2, 14, 16, 20, 41, 44, 51, 59] [15, 17, 21, 22, 31, 42, 52, 58]
H_Z (22 checks, sparse supports)
[0, 6, 21, 29, 31, 32, 33, 47] [1, 5, 11, 30, 32, 35, 37, 53] [2, 9, 13, 27, 33, 36, 37, 51] [3, 16, 24, 28, 34, 37, 38, 41] [4, 9, 17, 23, 35, 39, 42, 57] [5, 8, 18, 22, 36, 40, 43, 58] [6, 12, 15, 19, 37, 40, 42, 56] [7, 14, 22, 27, 38, 42, 44, 47] [2, 8, 15, 26, 31, 39, 41, 48] [0, 9, 24, 25, 40, 46, 49, 61] [4, 10, 20, 30, 40, 41, 45, 47] [3, 11, 18, 21, 42, 46, 48, 60] [1, 12, 17, 31, 38, 43, 49] [12, 13, 20, 25, 44, 48, 50, 53] [11, 14, 19, 26, 45, 49, 51, 54] [8, 16, 23, 46, 47, 51, 53] [5, 7, 17, 24, 33, 45, 48, 52] [2, 4, 18, 28, 32, 44, 49, 55] [10, 18, 19, 33, 34, 50, 57] [3, 17, 20, 29, 51, 55, 56, 58] [4, 12, 16, 21, 36, 52, 54, 59] [0, 22, 26, 28, 52, 53, 56, 57]
Code ID 62-18-7-b · download JSON · raw on GitHub